Propulsion Aspects of Large Sailing Yachts
Propulsion Aspects of Large Sailing Yachts
G.J.C. Nijsten*, J. de Vos**
Abstract
The present work forms part of a broader study into the performance of large sailing yachts. The study is driven
by developments in commercial shipping projects and environmental conservation projects. The vessels of these
projects require a (high) continuous speed, large operating range, low crew numbers and of course low fuel
consumption. In many situations sails and engines are used simultaneously. In addition to this the sheer size of
the rigs is increasing although it is required that these can be handled by a minimum of crew. Due to these
factors, the optimal main dimensions and rig type differ from conventional designs. In order to be able to
compare the designs mutually, an Excel-based computer program has been developed in which the performance
of these vessels can be evaluated.
Performance calculation is split into a velocity prediction while sailing and a thrust prediction while sailing
engine assisted. Velocity prediction is done in the conventional way; force and moment equilibrium are solved
for specific wind circumstances. Thrust prediction while sailing on engine and sails is done by an adjustment in
the VPP; force equilibrium is calculated at constant speed. Needed engine power and fuel rate can then be
computed, based on the propeller and engine properties.
With the aid of this program and a routing sheet, four different rigs are compared: Aerorig, Dynarig, 3-mast
schooner and a sloop. The criteria are minimal fuel consumption and minimal voyage time.
The described program makes it possible to evaluate various designs in an earlier design stage and to get a better
insight into aspects of the sail assisted mode. It is suitable for a broad range of designs and by its flexible
structure, the user can easily adjust several aspects to his own requirements without being a programmer.
1 Introduction
In the past years, the trend in big sailing yachts led to other design requirements. The vessels often use sails and
engines simultaneously. In addition to this the sheer size of the rigs is increasing although it is required that these
can be handled by a minimum of crew. Therefore, the optimal main dimensions and rig type differ from
conventional designs. The consequence is that requirements sometimes exceed the designer’s experience and
knowledge-based sense for dimensions and that the optimization of main dimensions is more and more a topic of
the earlier designs stages.
Until now only rather simple calculations were done on propulsion by engine and sails together. Hansen (1996)
gives an overview of wind ship activities and research over the past 30 years. These past researches aimed most
of the time on big cargo vessels rather than sailing vessels that are designed in the
first place to be propelled by sails. There was no systematic tool that could deal with a whole wind range and
that could easily compare different rigs or hulls. Furthermore with respect to velocity prediction while sailing, it
was desirable to have a more flexible calculation method in which for example measured resistance and
propulsion data or deviating resistance parts could be added by the user himself. To meet these demands, an
Excel-based program has been developed at Gerard Dijkstra & Partners.
The main purpose of this paper is to describe this Excel-based calculation method for performance comparison
of a vessel that makes use of sails or sails and engine together. Performance is defined as a velocity prediction
while sailing and a thrust prediction while sailing engine assisted at a constant speed. It will be explained how
performance of different designs can be computed and how these designs could be compared. Furthermore, to
show the possibilities of the program, four different rig types suitable for large yachts are compared.
*
**
Graduate Student, Delft University of Technology
Gerard Dijkstra & Partners
1
Propulsion Aspects of Large Sailing Yachts
One of the starting points of the developed program is that resistance is calculated according the Delft
Polynomials, although hull ratios exceed the DSYHS (Delft Systematic Yacht Hull Series) dimensions. Some
attention will be paid to this in the description of the VPP (Velocity Prediction Program). Furthermore, added
resistance due to waves (Raw) is not included yet. Calculation of Raw with the polynomials results in an
overestimation of this resistance part and is therefore omitted. Which, at this time, is not of major importance
because the main goal of the program is to use it for comparative purposes and not to produce absolute numbers.
The first part of this paper describes both the VPP and TPP (Thrust Prediction Program). Attention is paid to the
solved equilibrium, the build up of the program and to the validation of the results. The second part gives a short
description of the calculation example with the VPP-TPP. The four different rigs are placed on one and the same
hull and are compared for one specific route. Passage time and fuel consumption are computed where average
speed is kept to a required minimum. Finally, some conclusions and recommendations are made on the program
and the rigs comparison.
2 Build up of the calculation tool
The VPP-TPP has been developed on a normal PC in an Excel-Visual Basics environment. This combination
lends itself excellently for a visual check of the calculations and intermediate steps. It is simple to use and also
flexible, allowing for user input of for example deviating resistance polynomials or other relations in the
equilibrium equations (see also Martin, 2001). During the development of the program, more people have been
working on it, one after each other. It was a must that the structure of the program would not be too complicated
and that new applications could be easily added. The present structure of the program makes that possible.
The program exists of a VBA (Visual Basic for Applications) part and an Excel part. The latter is used as the
interface with the user; it contains input and output sheets. The actual velocity prediction and thrust prediction
calculations are done by the VBA part. Velocity and thrust prediction are separated and can be run
independently.
Main features of the velocity prediction
The VPP is based on force and moment equilibrium in x direction. The formulation is based on the equations
used in WinDesign (see Wolfson Unit, 1995). Figure 1 outlines this equilibrium. The rudder balance of the yacht
is not taken into account.
Fy
t
Fs,
Ls
Fx
course
heading
Vaw
Vtw
tw
Rt
aw
Ds
Vs
t
Fh,
Figure 1 Force
and moment equilibrium of the VPP
Equilibrium can by simply formulated as:
FH ,t = FS ,t
M righting = M heeling
2
Propulsion Aspects of Large Sailing Yachts
With:
FH ,t = Fs + Rt
FS ,t = Ds + Ls
M righting = ∇ ⋅ ρ ⋅ g ⋅ GZ
M heeling = FS ,t ⋅ (Z ce + Z clr )
With:
FH,t
Fs
Rt
FS,t
Ls
Ds
Zce
Zclr
Total force on the hull
Side force on the hull
Total resistance of the hull
Total force on the sails (windage of hull and rig included)
Lift force of the sails
Drag force of the sails
Vertical center of effort of the sail plan
Vertical center of lateral resistance
A schematic flow chart of the program can be found in the appendix, figure 1. The program is built up in such a
way that all resistance calculations are done in the Excel part, so there can be easily checked whether the various
resistance parts show a normal trend. The VBA part of the program loads all data from the input sheets into the
computer memory and then solves the equilibrium of hydrodynamic and aerodynamic forces and moments. It
varies reef and flat to find the best boat speed. The program solves the equilibrium by means of a simple iteration
module in which boat speed and heel are varied. The aerodynamic model in the program is based on the same as
used in the Windesign VPP (Wolfson Unit, 1995), the hydrodynamic model is based on the DSYHS (Keuning,
1998). The found optimum values for reef, flat, boat speed and heel at the concerned wind speed and wind angle
are plotted in the Excel output sheet.
Validation of the VPP
Three parts should be validated to check whether the program is usable for comparative studies. These are the
aerodynamic module, the hydrodynamic module and the “solver” module. The aerodynamic module is based on
simple equations derived from aerodynamics and are commonly used in yacht design, see also Wolfson Unit
(1995). No close validation exists for this part.
As already stated, the concerned hull dimensions and ratios exceed the range of hull parameters tested in the
DSYHS, so it is questionable whether the polynomials can be applied. In Nijsten (2002), there is done a
comparison for the various resistance parts (frictional, residual etc.) with model tests of the "Athena hull" (3
mast topsail schooner, Lhull = 80 m). From this, it became clear that the calculation according the polynomials
give a good fit with respect to the upright resistance without leeway (see figure 2). As for the heeled and yawed
cases, the tested and computed values show a good match. The mean difference is about 3 %.
3
Propulsion Aspects of Large Sailing Yachts
Tested and computed resistance components compared (no heel and leeway)
325000
Tested Rtu
Tested Rrt
Tested Rvt
275000
Computed Rtu
Computed Rrt
Computed Rft
225000
R (N)
175000
125000
Main dimensions:
Displacement
Lwl
Bwl
Tcanoe
Lwl/Bwl
1/3
Lwl/displ
Rtu
Rrt
Rft
829
61.4
11.5
2.7
5.5
6.7
tons
m
m
m
m
m
total upright resistance
total residuary resistance
total frictional resistance
75000
25000
0.05
0.1
0.15
0.2
0.25
Fn (-) 0.3
0.35
0.4
0.45
-25000
Figure 2 Upright resistance comparison of a hull that exceeds the range of hull parameters tested in the DSYHS
To validate the method of solving the equilibrium, the velocity prediction with the TPP-VPP is compared with a
prediction according the Windesign VPP. This program is chosen because it uses the same aerodynamic module
and has got various hydrodynamic modules, including the DSYHS polynomials. Furthermore, it is commonly
used and application of it showed already that the program is suitable for comparative studies, which is also the
goal of the VPP-TPP. A detailed explanation can be found in Nijsten (2002). There is concluded that, in spite of
a few differences, the velocity prediction according the Excel-VPP is suitable for comparative purposes. It must
be emphasized that any agreement with another VPP does not imply that the program yields accurate absolute
prediction of the performance. No comparison has yet been made with actual boat data.
Main features of the thrust prediction
The build up of the thrust prediction part of the program is similar to the VPP. Figure 3 shows the forces in x and
y direction. Total driving force Fx is now a summation of sail driving force and engine force. The TPP calculates
the needed "engine force" for a required constant speed. There is assumed that the added engine thrust only
affects this total driving force in x direction and that no differences occur in the moment equation. So:
Rt = Fx ,sails + Fengine
With:
Fx sails
F engines
Rt
Sail force in x direction
engine force, assumed to be in x direction only
Total resistance of the hull
4
Propulsion Aspects of Large Sailing Yachts
Ls
es
x engin
Sails+F
Fx= Fx
Ds
Rt
course
heading
Vtw
Vaw
tw
Fs,t
aw
Fy
Vs
Fht
Fs
Figure 3 Force and moment equilibrium of the TPP
A schematic flow chart of the TPP is included in the appendix, figure 2. It is required to adopt desired Vs in the
input sheet. During the calculation, this speed is kept constant and iteration is done with heel only. The output is
a minimal needed thrust for the concerned wind speed and wind angle. A negative equilibrium thrust, which
means that driving force by sails is bigger then the resistance at the required speed, results in zero engine thrust.
In this case, equilibrium speed lies above the required boat speed, which is calculated in the VPP. In some cases,
a minimum thrust is calculated at less then the minimum flat and reef values, for example in case of a really
small true wind angles. Consequently, the program sets sail power to zero (the sails are down) and the total thrust
is equal to the total resistance.
Polar Thrust diagram at constant boat speed
Resistance to overcome (kN)
10
90
20
30
40
70
50
6
8
10
12
16
20
50
60
70
30
80
10
0
0
20
40
60
80
-10
100
-30
110
120
-50
130
25
140
-70
150
160
Figure 4 Example of a polar thrust diagram at constant boat speed of 15 kts.
5
Propulsion Aspects of Large Sailing Yachts
The figure above shows a typical thrust diagram, required boat speed is 15 kts. Because the TPP is based on the
same calculations and modules as the VPP, it can be assumed that the calculated thrusts are of the same size as
the forces in the VPP, and thus should be useable for comparative purposes. It must be emphasized that this
does not imply that the program yields accurate absolute prediction of the performance. No comparison has been
made with actual boat data. The structure of the program is such that TPP and VPP run totally independent of
each other, so they could be run separately and calculation time could be kept to a minimum.
The calculated engine thrust can be expressed in a fuel rate per hour by means of simple relations. For one
specific engine and propeller, a relation between needed thrust (T) and propeller efficiency (ηe) is derived
(Nijsten, 2002). Here, the propeller characteristics of the controllable pitch propeller are approximated with a
propeller diagram of a B series propeller. For every wind circumstance (thus needed thrust), the pitch of the
propeller is adjusted so that the working point of the engine lies on the p-curve of the engine. This results in a
linear relation that is used to express the force (to be delivered by the engine) in a braking power (PB) at the shaft
and a fuel consumption rate (φmb).
Route calculation
The route sheet is based on a Trans-Atlantic crossing, New York to Landsend. The sheet is used to eventually
quantify the performance of the rigs in terms of crossing time and total amount of fuel consumption. The beneath
calculation is based on the study on an action vessel for Greenpeace. In this study, a minimum boat speeds was
required during a certain crossing and fuel consumption should be kept to a minimum. Fuel consumption
consists of fuel used for propulsion only and is an indicator for the performance of a certain rig.
In the route calculation, data from Pilot Charts is put into a spreadsheet. For a certain month, the course time
percentage for a range of wind speed and wind angle combinations is calculated (see table 1). With this matrix
and a calculation according the VPP-TPP, crossing time and total fuel consumption can be calculated. For every
wind speed - wind angle range, an average maximum boat speed and fuel rate is computed.
Btw
0 to 40
40 - 44
44 - 48
48 - 55
55 - 65
65 - 75
75 - 85
85 - 95
95 - 105
105 - 115
115 - 125
125 - 135
135 - 145
145 - 155
155 - 165
165 - 180
2 to 6
0
0
0
1.26
1.67
0.52
0.37
1.04
0.71
0.33
1.04
0.82
0.82
3.01
0
0
11.6
7 to 8
0
0
0
0
2.97
0.63
0.74
0.33
0.41
0.56
0.63
0.30
0.30
2.23
0
0
9.1
Vtw
9 to 10 11 to 12 13 to 14 15 to 17 18 to 21 22 to 26 27 to 31 32 to 36
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.11
0.26
0
0
0
0
1.34
1.52
0.93
0.04
2.45
2.75
2.56
3.68
2.08
0.63
0.19
0.11
0.56
0.56
0.63
0.82
0.85
0.33
0.33
0.11
0.41
0.22
0.56
0.56
0.37
0.45
0.30
0.11
0.74
0.48
0.71
0.59
0.93
0.74
0.48
0.15
0.48
0.89
0.82
0.74
1.19
0.45
0.52
0.07
0.78
0.48
0.74
0.78
0.97
0.82
0.33
0.19
0.78
0.45
0.74
0.74
0.63
0.74
0.15
0.15
0.59
0.71
0.52
1.08
1.15
0.85
0.52
0.19
0.67
0.63
0.74
1.30
1.23
0.67
0.82
0.26
2.82
2.30
2.64
3.60
1.93
1.19
0.33
0.26
0
0
0
0
2.27
2.71
1.45
0.59
0
0
0
0
0
0
0
0
10.3
9.5
10.7
13.9
14.9
11.1
6.5
2.5
Total
%
0.0
0.0
0.4
5.1
19.1
5.3
4.1
6.2
6.3
6.0
6.1
6.7
7.4
20.3
7.0
0.0
100.0
Table 1 Course time percentage during a Trans-Atlantic crossing (2765 nm), New York –Landsend
3 Application of the calculation tool
With the aid of the VPP-TPP and the routing data, a calculation example is done on several rigs. In this example,
four different rigs are placed on one and the same hull and performance during a transatlantic passage is
calculated. Main goal is to show the possibilities of a program such as the VPP-TPP and to illustrate the
broadness of its application.
To find out which rig is most suitable for the given route, two parameters are adopted as a performance
indicator: voyage time and amount of fuel consumption. Hereby is assumed that a minimum boat speed of 15 kts
is sustained. So sails and engines are used simultaneously at lower wind speeds.
Description of the hull and rigs
The hull is derived from a preliminary study on an 85 m action vessel for Greenpeace. The main dimensions are
stated in the following table.
6
Propulsion Aspects of Large Sailing Yachts
Canoe body:
Volume
Displacement, total
Tmax (T total)
Lwl
Bwl
Cb
Cp
Cm
LCB
LCF
waterplane area
wetted surface
941.53
1054726
6.57
82.301
12.290
0.384
0.528
0.727
45.256
48.304
682.571
780.239
m3
kg
m
m
m
m
m
m2
m3
Keel:
Volume
Span
Croot
Ctip
Cmean
thickness
Vertical center of buoyancy
wetted surface
84.53
4.15
24.29
21.02
22.65
1.54
1.94
197.40
m3
m
m
m
m
m
m
m2
Rudder:
Volume
Span
Croot
Ctip
Cmean
thickness
2.95
4.73
3.80
2.78
3.29
0.36
m3
m
m
m
m
m
Table 2 Hull dimensions of the 85 m vessel
The rigs, see figure 5, are still in development or already applied: sloop rig, 3-mast schooner rig, 3-mast Dynarig
and 2-mast Aerorig. The 3-mast schooner rig is derived from for the Athena design. The Dynarig was developed
in the 60ties by Mr. W. Prölls. It was in the oil crisis that he believed the Dynarig could be used as additional
propulsion. The Dynarig is actually a square rig. It has a freestanding mast with yards directly fixed to the mast.
The yards already have camber in them unlike the traditional straight yards. The sails are furled onto a mandrill
inside the mast. Trimming is done by rotating the entire mast. The Dynarig does not have the disadvantages of a
traditional square rig; no limits in bracing angle because there isn't any rigging, sails have better shape due to the
curved yards and higher efficiency because there are no gaps between the sails so that they work as one. More on
the Aerorig can be found in McDonald (1996).
Figure 5 Schematic sail plans , equal sail area = 2000 m 2
For simplicity, all the rigs are scaled to the same sail area, 2000 m2. The total displacement (thus the draught) of
the vessel is kept constant by reducing ballast for the heavier rigs. The stability of the vessel is also adjusted
according to the weight and center of gravity of the rig. This means that for example the stability of the sloop rig
drops due to reduction of the ballast and also due to the high VCG of the rig.
Calculation results
Table 3 sums the total crossing time and fuel consumption for the four rigs. Figure 3 and 4 in the appendix show
the polar boat speed and polar fuel rate diagram for 8 and 19 kts true wind speed. It is clear that the Aerorig
performances the best for the given route. Both crossing time and fuel consumption are lower then with the other
rigs. Striking is that with the sloop, the optimal thrust is always achieved with a combination of sails and engine
together (resulting in 0 % of the time on engine alone), although the other rigs show a percentage around 7 % on
7
Propulsion Aspects of Large Sailing Yachts
engine alone. This is caused by the wind speed- wind angle distribution and the fact that the sloop performs best
on sails and engine together. Only at really small wind speed-high wind angle combinations it is optimal to sail
on engine alone. The high fuel consumption of the 3-mast schooner is mainly caused by the huge amount of
windage and also by its low up wind performance. Because the Dynarig and Aerorig produce less side force and
have a low center of effort, they are characterized by a big sail carrying capacity when reaching, which suites the
given crossing weather profile.
Again there must be emphasized that added resistance in wave is not included in the calculations.
Transatlantic crossing
average time
average distance
total fuel consumption
minimal sustained boatspeed
percentage of time:
sails:
engine and sails:
engine
Rig
hrs
days
nm
tons
kts
3 mast sch. Dyna rig
2000 m2 2000 m2
175.36
172.94
7.31
7.21
2765.00
2765.00
17.52
15.12
15.00
15.00
%
%
%
26
65
8
32
61
7
Aero rig
2000 m2
170.28
7.09
2765.00
12.05
15.00
Sloop
2000 m2
176.62
7.36
2765.00
15.51
15.00
39
55
6
26
74
0
Table 3 Total crossing time and fuel consumption during the transatlantic crossing
4 Discussion
Although figure 2 shows a match for a hull that exceeds the Delft-series, more model tests should be done on
yachts with higher length-beam and length-displacement ratios. Until now only few test data is available and
uncertainties exists between the calculated values and actual boat data. Future research should furthermore aim
on a polynomial description of the added resistance in waves for bigger yachts. This could be done in the same
way as is done for the present DSYHS; a polynomial is derived from added resistance as calculated with the strip
theory program “Seaway”.
A further optimization of the program could lay in the use in a standard Excel solver as in Martin (2001). This
could reduce calculation time further. This solver could also be used for the build in of an optimization tool,
which could optimize the main dimensions of the rig and hull.
With respect to the example, results depend totally on the choice of weather profile. The example is not meant to
quantify the rigs but purely meant to show the possibilities of the program.
For the sail-assisted mode, the used linear relation between propeller efficiency and propeller load is only valid
in the circumstances as given. This means only valid for the adoptions with respect to the propeller diagram,
interaction coefficients and efficiencies of the propulsion installation. A broader derivation and a better insight
into the adoptions could make the program more flexible.
With this in mind, a program like the VPP-TPP could eventually be used for prediction of the actual boat
performance instead of for comparative studies only.
5 Conclusions
The described program makes it possible to evaluate various designs in an earlier design stage and to get a better
insight into aspects of the sail-assisted mode. Although the concerned hull ratios exceed the present DSYHS,
relatively good similarity exists between measured and calculated resistance of a hull that exceeds the series.
This, and the match with an existing VPP, makes the Excel-VPP TPP suitable for comparative studies.
The program is suitable for a broad range of designs and by its flexible structure, the user can easily adjust
several aspect to his own requirements without being a programmer. The calculation example with the four
different rigs shows that, together with routing data, a good quantification can be made of the performance of a
(engine-assisted) sailing yacht.
8
Propulsion Aspects of Large Sailing Yachts
References
Hansen, Knud E., Modern Windships, Part 1. Knud E. Hansen A/S, Consulting Naval Architects And Marine
Engineers, Copenhagen, 1996.
Keuning, J.A., and Sonnenberg, U.B., Approximation of the Hydrodynamic Forces on a Sailing Yacht based on
the ‘Delft Systematic Yacht Hull Series’. Delft: Faculty of Mechanical Engineering and Marine Technology, Ship
Hydromechanics Laboratory, Delft University of Technology, 1998.
Martin, D.E., and Beck, R.F., PcSail, a Velocity Prediction Program for a Home Computer. University of
Michigan, 2001.
McDonald, N., and Damon, R., Aerorig, The Rig of the Future. In: 14th International Symposium on “Yacht
Design and Yacht Construction”, Amsterdam, 1996.
Nijsten, G.J.C., Performance study on a Large Sailing Vessel. Delft: Faculty of Mechanical Engineering and
Marine Technology, Ship Hydromechanics Laboratory, Delft University of Technology, 2002.
Wolfson Unit, VPP for Windows, Windows-based Professional Systems for Yacht Performance Prediction. User
Guide 2.2, Wolfson Unit, University of Southampton, 1995.
9
Propulsion Aspects of Large Sailing Yachts
Appendix
Schematic flow chart, velocity prediction
START
Get input data:
geometry hull and rig, sail
coefficients, starting vs,
heel
ITERATION MODULE Boat Speed:
ITERATE
equilibrity
H and Vs
Starting value :
Reef =1
Starting value :
Flat =1
Input data:
Btw,Vtw,Flat,Reef
Starting values for Vs and
Heel
ITERATE
equilibrity
Heel and Vs
Flat
Flat_min?
FALSE
Flat= 1 - Flat_step
Reef =
1 - Reef_step
Calculate Sail driving force,
sail side force and heeling
moment
TRUE
Calculate optimal Flat from
Flat-Vs matrix
Calculated new Heel from
heeling moment and
stability curve
ITERATE
equilibrity
Heel and Vs
Change input
Vs and Heel
Calculate resistance parts,
dependend on heel etc.
Reef =
Reef_min?
Calculate new Vs
dependend on upright
delta resistance part
FALSE
TRUE
Calculate optimal Reef
from Reef-Vs matrix
Is Vs equal
to input Vs?
ITERATE
equilibrity
Heel and Vs
FALSE
TRUE
FALSE
Flat =
Flat_min?
Flat= 1 - Flat_step
Is Heel equal
TRUEto input
Heel?
TRUE
Calculate optimal Flat
from Flat-Vs matrix
TRUE
ITERATE
equilibrity
Heel and Vs
Plot Vs, heel, leeway etc.
in Excel sheet
END
Figure 1 Schematic flow chart of the VPP
10
FALSE
Propulsion Aspects of Large Sailing Yachts
Schematic flow chart, thrust prediction
at constant boat speed
START
Get input data:
required Vs, geometry hull
and rig, sail coefficients,
starting heel
ITERATION MODULE Needed Thrust:
ITERATE
equilibrity Heel
and needed thrust
Starting value :
Reef =1
Starting value :
Flat =1
ITERATE
equilibrity
Heel
Flat
Flat_min?
FALSE
Flat=
1 - Flat_step
Input data:
Btw,Vtw,Flat,Reef,
required Vs and starting
values for Vs and Heel
Reef =
1 -Reef_step
Calculate Sail driving force,
sail side force and heeling
moment
TRUE
Calculate optimal Flat from
Flat-Needed thrust matrix
Calculated new Heel from
heeling moment and
stability curve
ITERATE
equilibrity Heel
and needed thrust
Change input
Heel
Calculate resistance parts,
dependend on heel etc.
Reef =
Reef_min?
FALSE
Calculate Needed thrust to
sustain required Vs
TRUE
Calculate optimal Reef
from Reef-Needed thrust
matrix
Is Heel equal
to input
Heel?
ITERATE
equilibrity Heel
and needed thrust
FALSE
Flat =
Flat_min?
TRUE
Flat= 1 - Flat_step
TRUE
Calculate optimal Flat
from Flat-Needed thrust
matrix
ITERATE
equilibrity Heel
and needed thrust
Plot needed thrust, heel,
leeway etc. in Excel sheet
END
Figure 2 Schematic flow chart of the TPP
11
FALSE
Propulsion Aspects of Large Sailing Yachts
Polair diagram for 4 rigs at 2 wind speeds
22
Boatspeed (kts)
20
10
Sloop Vtw=8kts
30
20
18
Aero Rig Vtw=8kts
40
16
3 mast schooner Vtw=8kts
50
14
Dynarig Vtw=8kts
12
60
Sloop Vtw=29kts
10
Aero Rig Vtw=29kts
70
8
6
3 mast schooner Vtw=29kts
80
4
Dynarig Vtw=29kts
2
0
0
0
2
4
6
8
10
12
14
16
18
20
22
-2
-4
100
-6
110
-8
-10
120
-12
-14
130
-16
-18
140
-20
-22
150
170
160
Figure 3 Polar diagram of the rigs, 2 true wind speeds
12
Propulsion Aspects of Large Sailing Yachts
Polar fuel rate diagram at constant boat speed, 4 rigs, 1 Vtw
Fuel Rate (L/h)
10
270
20
30
Sloop Vtw=8 kts
40
220
Aero Rig Vtw=8 kts
50
3 mast schooner Vtw=8 kts
170
60
Dynarig Vtw=8 kts
120
70
70
80
20
0
0
50
100
150
200
250
-30
100
-80
110
-130
120
130
-180
140
-230
150
160
-280
170
Figure 4 Polar fuel rate diagram of the rigs, 1 true wind speeds, Vs = 15 kts
13
Propulsion Aspects of Large Sailing Yachts
14